X-ray microscopy has the potential for ultra-high resolution due to the very low diffraction limit, and penetration through thick samples. The trade-off is a lack of contrast in aqueous soft tissue samples. Following our development of phase-contrast imaging technologies broadband x-ray sources in a parallel project, we are re-assessing at a fundamental level the possibility of resolving soft tissue structures, such as cellular organelles, without incurring high radiation doses. Although there are promising technologies for phase-contrast x-ray microscopes, a careful consideration of what the fundamental limits of phase contrast and resolution may lie and what are the suitable applications in biological imaging is a necessary first step before the engineering effort begins.